physics.fluid.hydraulic_jump

O2: sequent depth y2/y1 = ½(−1+√(1+8 Fr₁²)) vs a separate-module identity (≤2 ULP). Not trapezoid jump, not specific energy alone, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated hydraulic-jump vectors. Not trapezoid jump, not Manning, and not Q=Av.

This summary records the outcome of the verification run. The full test corpus, oracle implementations, reference tables and generators are retained privately. Their digests identify those artifacts; a digest alone does not let a reader independently reproduce the full verification run.

Recorded result

8/8 passed

Oracle

O3 · mpmath 1.4.1

Reference table commitment (SHA-256)

31cbb90651a81f888bc2648182c0ac212e66f5c9c0b50cd57a6ec039dd7c4362

Generator commitment (SHA-256)

a17c25063d8aba4d38ac60c6a95d3734a7fac11a24f08b98d8d7ff918d5e29ed

Check a calculation

Use the capability's public input schema and examples to call the versioned REST API or MCP. These interfaces remain available without downloading the validation infrastructure. A successful example checks that example; it does not establish that the complete private suite has been independently reproduced.